How do you find the Maclaurin series for 1/(1+x^3)?

1 Answer
Dec 26, 2016

1-x^3+x^6-x^9+x^12-x^15+cdots for |x|<1.

Explanation:

The quickest way to derive the answer is to view 1/(1+x^3) as the sum of a geometric series. That is, use the formula a+ar+ar^2+ar^3+cdots=a/(1-r) when |r|<1.

In the given situation, a=1 and r=-x^3. Therefore,
1/(1+x^3)=1-x^3+x^6-x^9+x^12-x^15+cdots for |-x^3|<1, which is equivalent to |x|<1